Stable allocations: from theory to practice

This year’s Nobel prize in economics has been awarded to two game theorists, Lloyd Shapley (89) and Alvin Roth (60) for their work on a central economic problem: how to match different agents as well as possible. We dig deep into their work

What is game theory?Game theory is a branch of mathematical economics first theorised by Jon Von Neumann in the 1930s. It involves the principles of probability in a multi-player world where each player (agent, firm, etc) attaches a certain probability to the other players’ behaviour to an action he himself undertakes.

Which are the areas of application of game theory?Game theory is applied in several areas of current research including space sciences, engineering, stock markets, auctions, multi-firm bids in corporate mergers and acquisitions, and even in geo-political diplomatic strategies of war and peace.

How does it work?Game theory has several branches: Cooperative Games, Non-Cooperative Games, Strategic Games, etc. Its work can be best explained in the context of auctions. An auction is a non-cooperative game involving several players. Each player assumes that other players would react in a certain way for every action of his. A game of chess explains this more clearly. A chess player bases his moves assuming that his opponent would respond in a particular way and vice-versa. The strategies and tactics are based on these assumptions. In mathematics, these are called as “mixed probabilities” where the assumptions are based on an incomplete information of opponents.

Are there any specific examples that can be cited that has used game theoretic tools as mainstream corporate strategy?Yes, there are. The acquisition of a European steel maker by an Indian company in 2007 reflects the principles of a non-cooperative game theoretic strategy. After the bids were submitted, both the Indian company and its rival, a South American firm, were asked to participate in an auction to win the rights of ownership of the target company. As the auction began and reached the ninth round, the Indian company announced the tactic saying that it would bid five pence more than whatever the South American rival bids. The strategy was based on the probability that South American company would not bid beyond the certain point as the Indian company’s bid would anyway be higher by five pence than its rival’s. This move was based on the assumption that the probability of the rival continuing to bid beyond a certain level would be negligible. It turned out as planned. The probabilities were based on the financial muscle and other issues of the rival company, which the Indian firm had factored into the auction process.

What are the specific areas of work of this year’s Nobel prize winners?According to the Royal Swedish Academy of Sciences, Roth and Shapely have been awarded for their work that addresses key questions of day-to-day life. For example, students have to be matched with schools, and donors of human organs with patients in need of a transplant. How can such matching be accomplished as efficiently as possible? What methods are beneficial to what groups? In 1962, Shapley along with late David Gale in a paper titled “College Admissions and the Stability of Marriage,” explained how individuals could be paired together in “stable” matches that would last. Shapley used so-called cooperative game theory to study and compare different matching methods. Roth recognised that Shapley’s theoretical results could clarify the functioning of important markets in practice. The prize rewards two scholars who have answered these questions on a journey from abstract theory on stable allocations to practical design of market institutions.

What is Nash Equilibrium?Nash equilibrium, named after John Nash, Nobel prize winner and whose life the Oscar winning flick ‘A Beautiful Mind’ was based, is the solution to `game’ where each player thinks about his best strategy irrespective of what others would be doing. John Nash used a situation called the “Prisoners Dilemma” to students of psychology explain the concept, where in a closed cell, a prisoner would rather seek to maximise his gains than to “cooperate”.